What sort of cheating issues were those?
Well, the way I did mine was, I had polls for readers to vote for each category, and then I also judged myself, so there would be a Reader's Choice and a Webmistress's Choice award for each category. I figured that was a nice compromise - then no one could accuse me of being biased or anything for the ones that were voted on, and I could also give stories that were really good but maybe not as popular/recognized awards.
I got fed up with the voting, though, because I noticed a select few stories by a select few authors who were all friends getting WAY more votes than any of the other stories, and it seemed very fishy to me, especially since I'd never even HEARD of any of those stories and authors before that season (and I'd been reading fanfic for probably four years at that point and had run my awards 3 or 4 times, so I was pretty familiar with the popular stories). I thought that my polls were the kind where you could only vote once a day, period, but after playing around enough, I discovered that if you restarted your whole computer, you could vote more than once a day, so I think they beat the system and ensured that they and their friends would win in all their categories.
Some of those people used to run their own awards, where, ironically, all of their friends would also win, and those were done by judging. And, to me, there was nothing that special about their stories, especially when compared to some of the others that were nominated. So I got fed up with awards altogether that year (and this was a few years ago; I don't think any of those authors are still writing anymore, so I'm not talking about anyone on AC or anything), and I haven't run mine since.